A roller coaster of mass 800 kg starts from rest at the top of a hill with 1,500,000 J of potential energy. It ends up at ground level moving at 45 m/s. How much energy was lost to heat and friction?

E_loss  = 690000 [J]

Explanation:

The principle of conservation of Energy tells us that energy is converted from Kinetic to mechanical when the body moves from the highest point to the point where the velocity is maximum. That is, all potential energy is transformed into kinetic energy.

Now we must determine the kinetic energy at the end, when the roller coaster is at the point where the reference point of power energy is zero.

where:

m = mass = 800 [kg]

v = 45 [m/s]

Now replacing:

Now by means of the difference of the energy at the beginning minus the final energy, it determines the amount of energy that is lost by the effects of friction and heat.